In last week’s Hatch, the report governing the likelihood of encounter of a tank-penetrating gun at any particular range was covered. It’s a two-part report, though, and the second part of it covers the likelihood that a tank will be struck from any particular aspect. i.e., is the tank even facing the gun which hit it?

So I turn the keyboard back over to the Ballistics Research Lab and whoever was doing the typing in late 1951.

Angular distribution.

The percentages of hits* on the various surface of knocked-out tanks appear in a British report, “A survey of Tank Casualties”. Extracts from this report giving percentages of hits on the front and rear of the hull and turret appear in Table II. The hull and turret are treated as separate units. Thus the percentages of hits on the front, sides and rear of the hull add up to 100%. The same holds for the turret. This break-down must be made since the hull and turret have two separate hit distributions. This is due to the fact that the turret is not always facing forward when hit.

Table II: Sites of hits on Allied tanks knocked out by A.P. shot in NW Europe during WWII

*Although ranges were given for tank casualties, angular distributions of hits were given, without reference to whether or not a hit produced a casualty.[Chieftain’s note: In other words, it would be possible for multiple hits to be accounted for on a single tank, some of which may have failed to penetrate, or some tanks may have suffered multiple penetrations before the opposition stopped shooting at them.]

The function chosen to express the angular frequency distribution of hits on the hull is:

Where θ = angle of attack in radians measured from the front of the hull.

[Chieftain: Bad news, guys. More maths follows]

The corresponding function for the turret is

Where θ = angle of attack in radians measured from the front of the turret.

These two functions can be written in the common form:

Where

a= constant = 1 when considering hits on the hull, ¾ when considering hits on the turret.

[End Extract]. I’m sure this means something to someone. There followed about 8 more pages of data and formulae, but the bottom line from it all was that about half of the hits on the hull came from the sector between the angles of 47° on each side of the front. The corresponding sector for the turret is between plus and minus 55°. See Figure 12 for a graphical depiction.

What is particularly interesting, and perhaps may seem counter-intuitive, is that it appears that turrets were more likely to be hit in the rear than hulls were. Something must have been attracting their attention, and there were overlapping sectors of fire involved. At least, that's how I would explain it.

In any case, the paper then attempted to make sense of the data. The “So what”, as it is perhaps known:

Range distribution and Terrain:

In the preceding sections, empirical equations were fitted to the range distribution of casualties and the angle of distribution of hits by German anti-tank guns and tanks on US and British tanks in NorthWest Europe. It was noted that the distributions of casualties in range for the three armies were about the same, although they represented operations in slightly different territory. This suggests that the range distribution of casualties is determined by some factor that influences all of the engagements in the same way. The following observations and deductions are offered as an explanation. Operational data shows the following things:

1. Four out of five engagements between single tanks were won by the tank that fired first.

2. The “Survey of Tank Casualties” showed that half of all casualties were caused by a single hit, and the average number of hit per casualty was less than two.

3. German weapons could perforate Allied armour in most cases out to 2,000 yards, whereas Allied guns could perforate German armor only out to 800 yards.

From these facts the following deductions can be made:

1. Few rounds were fired by a tank in an engagement on the average. If many rounds were fired by each of two combatants on the average, the importance of firing the first round would not be as high as indicated under 1 above.

2. If few rounds were fired to determine an engagement the single shot probability of hitting and killing must have been high. This corresponds to short ranges.

3. As noted earlier, the average range at which casualties were obtained was also short, and this is consistent with the above prediction that the battles took place at short ranges, that range change during a battle was small, and that the distribution of battle ranges and distribution of casualties should be about the same.

4. Because the Germans outgunned the Allied armor they would have preferred long battle ranges at which their armor would have protected them from Allied fire while their guns would still perforate Allied armor. Since such long battle ranges were not in fact observed, it is deduced that the Germans were prevented from engaging in long range combat either by Allied maneuver or by terrain. It will be shown in subsequent paragraphs that the distribution of battle ranges can be attributed to characteristics of the terrain.

[Chieftain’s note: This then diverged into seven pages of mathematical formulae showing exactly what they said it would. I understood so little, I didn’t spend time scanning them. Sorry. It then moved to Turret Theory.

The angular distribution of attack for the turret is different from that of the hull. Although the turret is faced with the same distribution of guns with respect to the forward direction of the hull, it is not always facing in that same direction. Thus the turret distribution depends on the direction in which the turret is facing when attacked.

A tank can assume three different attitudes towards an attacking gun. These attitudes describe the manner in which the turret is used.

A tank can assume a passive attitude. That is, the tank does not know the direction from which to expect an attack and it carries its gun in a forward position. Under these conditions, the angular distribution of attack is equal to the corresponding distribution for the hull.

A tank can be retaliating or engaging the attacking gun when hit. Only the front of the turret can be hit when this attitude is assumed.

Finally, the tank can assume an active attitude by engaging or expecting to engage a target other than the attacking gun. There is a distribution in the direction toward which the turret is facing when the tank is attacked.

The data from the Second British Army, previously quoted for the distribution of ranges also includes, where the information was available, the direction towards which the turret was facing and the conditions when the tank was knocked out. In only 3 of the 85 cases cited were the tanks actually engaging the gun that knocked them out. These 3.5% of retaliatory cases will be neglected. The direction towards which the turret was facing in the other 82 cases is shown in Fig 17. The ordinate represents the estimated turret azimuth in both the clock system of measuring angles as was used in the data, and in degrees. The abscissa gives the number of cases having this estimated azimuth. It can be interpreted as the number of cases within the 15° sector including that angle. The great number of cases at 0° shows that the turret was facing forward a good part of the time when the tank was hit. The 40 cases at 0° include all the passive as well as some of the active cases.

Figure 17 shows that, apart from what the situation is in this forward sector, the directions toward which the turret faced were spread around the tank with a tendency to cluster around the forward direction. It is reasonable to assume that this is a smooth distribution and that the number of active cases in the forward sector is roughly equal to the number in the adjoining sectors. Since there were 7 active cases at 11:00, 4 at 11:30, 3 at 12:30 and 4 at 1:00, it might be inferred that there were about 3-6 active cases at 12:00 and the remaining 34-37 passive.

[End extract]

Many more pages of incomprehensible mathematics followed.

So what does all this from this and last week’s article tell us?

Perhaps firstly, the importance of terrain. It would be highly instructive to see some sort of similar assessment of a similar time period on the Soviet front. Possibly as much by luck, the Western Allies went into battle with tanks quite well suited for the terrain in which it fought, where reaction time counted for more than long-range accuracy and hard survivability. Look out the nearest window, and try to figure out what’s within 350m, then imagine defenses set up in that band. Again, the average range of engagement is not the most likely range. Those occasional 2,000m shots tend to skew the average up a tad. That’s quite a wide angle to be covered, and it likely has a bearing on the second problem: Just how many times a tank was not shot at from the front.

Go back up to the table near the beginning of this article. More allied tanks were killed by going through the side or rear armor than front. An initial impression may well be “Well, duh. The front armour is thicker, it bounced more shots. If the front armour worked as advertised, the impacted tank wouldn’t be part of this survey of knocked-out tanks!” Perhaps, but there are several other points to note on this.

Firstly, the somewhat astonishing figure that only 3% of the killed vehicles of which their activities were known were engaging the weapon that killed them, which certainly brings into question the idea of a ‘tank duel’ as being common in Western Europe. There are a couple of different reasons which may be explain this.

Primarily, it is really hard to spot a threat, especially if you’re on the move. I would go as far as to suggest that the destruction of the tank was the first clue for a large portion of tankers that the enemy had them in their sights. Mechanised combat can be brutal and fast. The related figure was that about half the vehicles were in a ‘passive’ position, gun forwards.

Then, given the short nature of the typical engagement range, two enemies only 100m apart from each other, which is unusually close, will still provide quite an angle differential for the target vehicle. If the Allied tank is facing one enemy, the other enemy is already getting a pretty good look at the side of the allied tank. If in the ‘most likely’ engagement range of 330m, the Germans place a tank 300m from an anti-tank gun, which is not unreasonable, and the allied tank turns to face the German tank, that’s about 60 degree offset angle and a very definite opportunity for a shot into the side armor from the AT gun.

This is well and good for the Allies, but how does it affect the Germans? What conclusions can we draw from this data which is purely Allied-related? There are two very significant differences. Firstly, that the Allies were usually the ones advancing into the German engagement areas. Secondly, that some of the German vehicles were pretty tough nuts to crack from the front.

Perhaps the most important thing to consider is the likelihood that Allied tanks were not rolling around on their own. The fact that most of the killed allied tanks seem to have not known that their killers were out there leads to the conclusion that once battle was joined, far fewer allied tanks were lost. If it were a sustained fight, they would obviously be aware of the enemy. Again, several factors can account for this effect. By the way, for this whole section, I’m theorizing and extrapolating here, feel free to engage me on the forum and we’ll see if we can hammer something out.

Firstly, the fact that a late-war AT gun is a Die-in-Place piece of equipment. One is not going to be able to pick up and withdraw a PaK-40, or worse, a PaK-43 after firing a round or two. Shoot-and-scoot is not a possibility. Any engagement for a PaK is going to end one of two ways: Everything with sight to it is dead, or it goes down in a blaze of glory. Now, add to this the fact that any Allied tank is going to have friends, and those friends such as Shermans are going to have good broad fields of vision and fast target lay rates, and things don’t look good for the AT gun.

The above commentary on how only a few hundred meters separation can create a side shot also applies, of course, to the ambushing vehicles. A Jagdpanther facing a target vehicle and providing a very tough armoured target may well be providing a flank shot to that target’s platoon-mates... Who can then slew and deal with the target. This sort of effect is doubtless part of the reason that the US were so successful at Arracourt, where many German vehicles were presumably killed by side impact. It is not unreasonable to presume that in instances when the Germans were attacking, the ratio of hits on each aspect of hull and turret would be more or less similar to that of the Allied tanks above. That’s a lot of hits in the sides and rear, and the US had a lot of guns to make them.

In any case, if so many Allied tanks were destroyed without knowledge of being attacked, and so few were destroyed whilst dueling, the logical conclusion appear to me that the first kill on an allied tank in any particular engagement was also often the last kill on an allied tank in any particular engagement. What could result in this?

Again, there aren’t many ways for an engagement to end (All of the below can have Germans and Allies reversed):

First choice, the first volley by the Germans kills off all the Allied tanks and there is nothing left to either kill in a duel. Secondly, the first volley by the Germans kills off a number of Allied tanks, and their friends kill off the Germans in response. The next option is that the Germans or allies withdraw. In a few rare cases, an extended duel may occur. That’s about it.

The problem with the first circumstance is that, by and large and as mentioned above, the Allied tanks didn’t wander around on their own. After the first salvo, the remaining allied forces would have been well aware that there was something out there, and ‘passive’ attitudes would be over. This leads logically to the majority of incidents being either that the Allies destroy the Germans, drive them off, or fall back. Well, in the long term, the Allies didn’t do all that much falling back. Which of course leads us to destruction or withdrawal as the two most likely outcomes. For AT guns, withdrawal isn’t an option. I’d hate to be a PaK gunner. For vehicles, either is a possibility, but attrition from all those off-angle shots, or simply mobility kills, will eventually result in destroyed AFVs. And, besides, the infantry the tanks or TDs were supporting would not be happy, so they would likely withdraw as well. The Allied advance towards Germany would continue. And that was in circumstances where the Germans fired first. In the event that accompanying forces such as recon troops or infantry notified the Allies of German AT gun or AFV presence, the Allies could get that first shot off, or simply suppress the opposition by fires in order to maneuver.

Again, this is speculation on my part, but it is not unfounded. Basically, where I’m going with this is that an assessment of the data can lead to interesting lines of thought. One can imagine how, say, a British or French tank designer can use this information to design his tanks to best survive on a future battlefield on the same terrain, or perhaps a planner can use such data to better form his tactics. One can also use this data to do the reverse: Look at the designs of vehicles, and try to understand why the results were as they were. For example, why were Shermans considered to be more effective vehicles than Panthers, when normally the figures would say that they weren’t?

Anyway, Bob will bring you back to the forum thread. We’ll do a little less abstract work next time.

So basically, turret was pointed toward the front of the hull unless a direct threat had presented itself. Generally, by the time a direct threat had presented itself, the tank had either

A. Been fired upon, penetrated and rendered inoperable with everyone inside out of action.

B. Been fired upon, not penetrated or not fully out of action, and is suffering a rather significant emotional event and a curious smell in the fighting compartment.

From what I gather from the table:

Most engagements were over nearly as soon as they began. 40-60% of vehicles were knocked out before they realized they were under attack. Those that were lucky enough to not be penetrated or were missed entirely, assuming they then became immediately aware that they were actually under attack, were still unlikely to survive but allied armor could then act on the opposing force.

One item that I noticed that isn't included in this analysis is the effect that the battle tactics of the time would have on this data. When traveling, tanks don't all travel in a straight line with their turrrets facing forward. After the first tank, each tank has a sector of responsibility to keep an eye on that is either side of the direction of travel. This is true if they are advancing in echelon or in a wedge formation as well. So, the end tanks of a 4 tank platoon would have its turret exposed at 45-60 degree to the guns that are at the center of the advance when looking at a wedge. If a single file line of tanks was engaged by an enemy formation line abreast in front, there would be rear or side shots available on some of the tanks in the line. I am not sure if the Germans or allies had similar platoon formations that we do now but I would assume they are similar. I haven't researched small unit tank tactics in WWII but tank combat was new so I am sure the tactics really involved throughout the war.

Rommel had developed large unit tactics in the Desert campaign where the German tanks would attack and then retreat. The British would then counterattack right into the teeth of a kill zone of 8.8cm anti-tank guns and take horrific casualties. So, by the time we were fighting in Europe the German's were very adept at setting ambushes. With the excellent German guns, its not surprising at the high number of single shot kills. I have attached a link to the combat footage from Cologne during WWI where a Panther engages a Sherman and The Panther is engaged by a Pershing.

Thanks for the information. Like most I do not understand the math but the explanations are clear. Regarding the Pac's and the idea the battles could only end with all the enemy dead or the pac dead, you might add the enemy tanks would withdraw or bypass the area.

The problem I have with WoT's developers is almost all games are public battles. When we go into the battles we see the percent chance to win or lose if we have XVM. The developers at WG have the same stats and know those percentages are true at best.

For example if a team has a 30% chance to win at the start, which is not at all unusual with your matchmaker, it is almost a certainty to frustrating loss for the 30% underdogs before the match even starts! In fact I do not think I have seen a 30% team ever win or a 70% chance team ever be defeated.

It is all well and good to buff armor a millimeter or two, make a tank turret turn 2 degrees slower or whatever. However by far the biggest problem (and the huge elephant in the room) is the deciding of the battle before it even starts by the matchmaker.

Obviously what needs to be done is make a matchmaker that does not pile great players against the less talented and experienced ones.

It is great when a battle is around 50/50 or even 45/55 or some reasonable (and easily attainable) number. However many of the public 15 vs. 15 matches are so skewed they are decided by Wargaming developers and the players are almost guaranteed a win or a loss.

Since you all know these facts, and are refusing to address the skill problem, some are beginning to wonder if you are simply playing favorites and putting your favorites on dominant percentage teams. That sounds far-fetched to me. To me it seems more like it is just laziness and being stubborn. "We have always done it this way, we are the boss, and we are never changing" seems to be the developer's attitudes in this game.

Seriously, what is wrong with wanting a reasonably fair match. You move heaven and earth to try and figure out armor, penetration, maps, etc.

Yet the sad (sad) truth with WG is that many of the matches are so skewed by great players vs. bad players on teams your matchmaker renders all your hard work on armor, camo., etc. irrelevant.

I do not see how developers in good conscious can continue to do this to their player base. Bad percentage or great percentage matches make a travesty of an otherwise fantastic game.

Some will always be fanboys and rush to the defense of whatever group is in charge. That is foolish, as they simply prolong problems by tickling the ears of you guys. Some will say that ranked battles are the answer. Well, I bet not 1% of the total matches will be ranked battles compared to at least 95% of total matches being pubic matches. But I digress.

It would be good to have fair matches. Maybe a limit of 42% for a low team, and a high percent of 58% for the lucky, or better team. That is some easy to understand math. You do not even have to use physics to figure that out.

Thanks for reading. I look forward to seeing you on the battlefield on the same team or the other team even. But in a fair battle and not a 30% to 70% one.

Excellent point Supdox! I often wonder about this "loading" and I have a theory. As this has affected me (and pretty well everyone else!) both negatively and positively, Wargaming allows it to happen. Why? It's simple: Money (always follow the money). Players who end up on the wrong side of the battle from the get go and repetitively on a losing team then eventually decide that they have to purchase gold to buy APCR rounds (or of course use credits) or more importantly, buy a PREMIUM tank with real money. Wargaming makes money on such players (many) who become despondent about their poor win ratios and finally throw in the towel and buy a PREMIUM tank to help counter the losses suffered. After all some PREMIUM tanks see maximum tiers in battle and are cheaper to repair, lower ammo costs, etc.

I know, I have been such a victim and bought a couple of lower tier PREMIUM tanks. However now, I don't really care and play for fun but it still bothers me that there is no "fairness" in WoT because of skill loading being done.

Thanks, Chieftain! This is exactly the sort of information I enjoy receiving. I've been gaming WWII tank combat for over forty years, and my ongoing goal has been to better understand how tanks actually fought during that war, so I could make my simulations better. Data like these fill large voids in my understanding.

i like the article. i agree with others the real elephant in the room is matchmaker. it is not much fun to neither win or lose 13-0, and those happen frequently lately. and balancing teams by armor is not going to be as effective as balancing by skill level. so not only when playing tier 8 now in platoons, you are pretty much guaranteed to see tier 10 and never see tier 6, so how is that ballanced, but being low tier in my Mutz i feel like i have pretty much nothing to say in the game anymore. i can farm as much as i can, and the battle will go its course anyway, depending on top tiers heavily. and if you don't take skill into consideration, we end up with purple vs red top heavies as an example. don't take a genius to figure out what happens there. but hey, thank god they have same amount of armor i guess. you should know well the community is using wn8 as main skill indicator. while not perfect, it is considered one of the best indicators, and i never ever heard of anyone getting a player into game because of more armour. in fact better clans tend to use less armour in general, as tactics (skill) seem to win more battles than pure armor. if armor was so important, you would see every clan wars battle composed of maus tanks only, but it is not the case. instead, you see good clans composed of skilled players, right? so why would you consider balancing armour instead of balancing skill? yes, let rng do between 42% - 58% as previously suggested, all equal 50% would be boring after a while, but the recently common 30% - 70% is just not much fun. your matchmaker is broken, we all seem to agree skill is the factor to take into consideration when balancing, so for the love of god, armour, really? just wanted to let others know you are not alone there, and thanks to Supdox for bringing up this very important topic.

One item that I noticed that isn't included in this analysis is the effect that the battle tactics of the time would have on this data. When traveling, tanks don't all travel in a straight line with their turrrets facing forward. After the first tank, each tank has a sector of responsibility to keep an eye on that is either side of the direction of travel. This is true if they are advancing in echelon or in a wedge formation as well. So, the end tanks of a 4 tank platoon would have its turret exposed at 45-60 degree to the guns that are at the center of the advance when looking at a wedge. If a single file line of tanks was engaged by an enemy formation line abreast in front, there would be rear or side shots available on some of the tanks in the line. I am not sure if the Germans or allies had similar platoon formations that we do now but I would assume they are similar. I haven't researched small unit tank tactics in WWII but tank combat was new so I am sure the tactics really involved throughout the war.

Rommel had developed large unit tactics in the Desert campaign where the German tanks would attack and then retreat. The British would then counterattack right into the teeth of a kill zone of 8.8cm anti-tank guns and take horrific casualties. So, by the time we were fighting in Europe the German's were very adept at setting ambushes. With the excellent German guns, its not surprising at the high number of single shot kills. I have attached a link to the combat footage from Cologne during WWI where a Panther engages a Sherman and The Panther is engaged by a Pershing.

The whole point of an attempt to gather a large data set is to remove the tactical element from the equation. It simply isn't relevant to the points being drawn out: tanks tend to face known enemies and first shot usually wins. I will say that this is *exactly* what we were taught in the late 80's & early 90's in BAOR. It was drilled into us again and again and again: face the expected avenue of approach (which the infantry screening you are supposed to tell you) and make sure you take the first shot. Then, enjoy your ~90 minutes expected survival time.

There's actually a very accessible discussion on the subject of tactical tank combat and casualties in Max Hasting's book "Overlord". (Not as good a book as his one on the Korean War, but still an excellent read. (Boy, does he bag the Americans in Normandy on the tactics front!)) He discusses how the Germans actually employed their AT guns (either at long range in overwatch positions (where they *could* stay unseen and keep firing)) or, in closer terrain, in channel denial roles whereby they would act to simply block an advance and be capable of taking out the lead vehicles and then effecting an escape due to no one (alive) on the other side having an effective shot back at them.

one statistic i saw on shermans, that i havent been able to locate recently, is that only 25% or less of all their engagements involved enemy armor; and that they were more often tasked for artillery/indirect fire duty, than anti armor duty.

basically everyone tried to use their tanks against infantry, and only against armor if things went wrong. (ie defensive plays, or holdouts) I know one of your previous documents mentioned that the germans were very careful to not commit armor before infantry. Blitzkrieg was always a bit of a misnomer. it wasnt tanks charging ahead, it was infantry with combined arms support. their tanks came out only after the infantry ran amok of allied defenses.

basically everyone tried to use their tanks against infantry, and only against armor if things went wrong. (ie defensive plays, or holdouts) I know one of your previous documents mentioned that the germans were very careful to not commit armor before infantry. Blitzkrieg was always a bit of a misnomer. it wasnt tanks charging ahead, it was infantry with combined arms support. their tanks came out only after the infantry ran amok of allied defenses.

Bear in mind that German doctrine and tactics were not the same 43-45 as they were 39-42. The Germans declared Blitzkrieg obsolete as a formal doctrine in early 42. Remember, it wasn't a new doctrine per se even then - it was simply taking a 19th century Prussian doctrine (break the line using <whatever>, cavalry go through and rampage as fast and deep as poss) updated to account for modern vehicles and communications.

Bear in mind that German doctrine and tactics were not the same 43-45 as they were 39-42. The Germans declared Blitzkrieg obsolete as a formal doctrine in early 42. Remember, it wasn't a new doctrine per se even then - it was simply taking a 19th century Prussian doctrine (break the line using <whatever>, cavalry go through and rampage as fast and deep as poss) updated to account for modern vehicles and communications.

true, but better accounts show that it wasnt tanks charging through the lines. (ie cavalry). it was the infantry moving forward, spotting or eliminating enemy anti-armor/anti-tank weapons, then armor moved in to clear everything else that was a threat to the infantry. basically they were using armor as mobile field artillery, which is sorta backwards of the Hollywood idea of tanks blitzing through Europe.